Yang-Baxter sigma models and Lax pairs arising from $\kappa$-Poincaré $r$-matrices

Abstract

We study Yang-Baxter sigma models with deformed 4D Minkowski spacetimes arising from classical $r$-matrices associated with $\kappa$-deformations of the Poincaré algebra. These classical $\kappa$-Poincaré $r$-matrices describe three kinds of deformations: 1) the standard deformation, 2) the tachyonic deformation, and 3) the light-cone deformation. For each deformation, the metric and two-form $B$-field are computed from the associated $r$-matrix. The first two deformations, related to the modified classical Yang-Baxter equation, lead to T-duals of dS${}_4$ and AdS${}_4$\,, respectively. The third deformation, associated with the homogeneous classical Yang-Baxter equation, leads to a time-dependent pp-wave background. Finally, we construct a Lax pair for the generalized $\kappa$-Poincaré $r$-matrix that unifies the three kinds of deformations mentioned above as special cases.

31 pages, v2: some clarifications and references added, published version

References in corpus (19)

• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• On deformations of AdS_n x S^n supercosets
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
• Yang-Baxter sigma models based on the CYBE
• Chaos Rules out Integrability of Strings in AdS_5 x T^{1,1}
• Integrability of classical strings dual for noncommutative gauge theories
• A Jordanian deformation of AdS space in type IIB supergravity
• The ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ mirror model as a string
• Yangian symmetry in deformed WZNW models on squashed spheres
• Schrödinger geometries arising from Yang-Baxter deformations
• Hidden Yangian symmetry in sigma model on squashed sphere
• Double Wick rotating Green-Schwarz strings
• Chaotic strings in a near Penrose limit of AdS${}_5\times T^{1,1}$
• Integrable deformations of the AdS${}_5\times$S${}^5$ superstring and the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence --
• Anisotropic Landau-Lifshitz sigma models from q-deformed AdS_5 x S^5 superstrings
• Towards the gravity/CYBE correspondence beyond integrability -- Yang-Baxter deformations of $T^{1,1}$
• Lax pairs for deformed Minkowski spacetimes
• Real and pseudoreal forms of D=4 complex Euclidean (super)algebras and super-Poincare / super-Euclidean r-matrices

Cited by in corpus (9)

• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• On jordanian deformations of AdS_5 and supergravity
• Generalized type IIB supergravity equations and non-Abelian classical r-matrices
• Non-split and split deformations of AdS_5
• Kappa-Deformations: Historical Developments and Recent Results
• Sigma models with local couplings: a new integrability -- RG flow connection
• Yang-Baxter deformations and generalized supergravity -- A short summary
• Killing spinors from classical r-matrices
• Basic quantizations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries